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Newton - Zamorascience
Newton - Zamorascience

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Rotational Energy and Momentum

Lecture 5.1
Lecture 5.1

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Lecture 10 (Feb 15) - West Virginia University

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ANSWERS TO QUESTIONS

... There are friction forces at both contact surfaces—between the hand and the book on top, and between the book and the table underneath. If the friction force between the hand and the book is larger than that between the table and the book, the book will be dragged along by the hand. In this case sta ...
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Motion - Marion ISD

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Satellite Orbits

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Go over midterm, Springs

... an N# pair. Once again, you must look at the NET FORCE acting on the objects to determine what will happen to them. We must also take into account mass to determine what the accelerations will be; since the truck has greater mass than the car, with the net force on both equal, the truck will acceler ...
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Newton's theorem of revolving orbits



In classical mechanics, Newton's theorem of revolving orbits identifies the type of central force needed to multiply the angular speed of a particle by a factor k without affecting its radial motion (Figures 1 and 2). Newton applied his theorem to understanding the overall rotation of orbits (apsidal precession, Figure 3) that is observed for the Moon and planets. The term ""radial motion"" signifies the motion towards or away from the center of force, whereas the angular motion is perpendicular to the radial motion.Isaac Newton derived this theorem in Propositions 43–45 of Book I of his Philosophiæ Naturalis Principia Mathematica, first published in 1687. In Proposition 43, he showed that the added force must be a central force, one whose magnitude depends only upon the distance r between the particle and a point fixed in space (the center). In Proposition 44, he derived a formula for the force, showing that it was an inverse-cube force, one that varies as the inverse cube of r. In Proposition 45 Newton extended his theorem to arbitrary central forces by assuming that the particle moved in nearly circular orbit.As noted by astrophysicist Subrahmanyan Chandrasekhar in his 1995 commentary on Newton's Principia, this theorem remained largely unknown and undeveloped for over three centuries. Since 1997, the theorem has been studied by Donald Lynden-Bell and collaborators. Its first exact extension came in 2000 with the work of Mahomed and Vawda.
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